What is the Least Common Multiple of 39600 and 39609?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 39600 and 39609 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39600 and 39609, than apply into the LCM equation.

GCF(39600,39609) = 9
LCM(39600,39609) = ( 39600 × 39609) / 9
LCM(39600,39609) = 1568516400 / 9
LCM(39600,39609) = 174279600

Least Common Multiple (LCM) of 39600 and 39609 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39600 and 39609. First we will calculate the prime factors of 39600 and 39609.

Prime Factorization of 39600

Prime Factorization of 39609

Now multiplying the highest exponent prime factors to calculate the LCM of 39600 and 39609.

LCM(39600,39609) = 2⁴ × 3⁵ × 5² × 11¹ × 163¹
LCM(39600,39609) = 174279600